Derivatives

Product Rule

100

y = (2x+1)(x²+1)

What is dy/dx = (2x+1)(2x)+(2)(x²+1)

200

y = (e^x)(x²)

What is dy/dx = (e^x)(2x)+(x²)(e^x)

300

y = 2e^3xsqrt(x)

What is dy/dx = e^3x/sqrt(x) + 2sqrt(x)(3e^3x)

400

y = sin(x)e^4x(2x³-4x)

What is dy/dx = sin(x)e^4x(6x²-4)+(2x³-4x)[(4sin(x)e^4x+cos(x)e^4x]

500

y = sec(x)(5x⁴+2x²)(x+3)

What is dy/dx = sec(x)[(5x⁴+2x²)+(x+3)(20x³+4x)]+sec(x)tan(x)(5x⁴+2x²)(x+3)

Quotient Rule

100

y = x²/(x+3)

What is dy/dx = [(x+3)(2x)-(x²)]/(x+3)²

200

y = sin(x)/x

What is dy/dx = [xcos(x)-sin(x)]/x²

300

y = tan(x)/e^x

What is dy/dx = [e^xsec²(x)-tan(x)e^x]/e^2x

400

y = e^2x(x²+1)/(x-3)

What is dy/dx = [(x-3)(e^2x(2x)+2e^2x(x²+1))-e^2x(x²+1)]/(x-3)²

500

y = 2x/[e^xcot(x)]

What is dy/dx = [2e^xcot(x) - 2x(e^x(-csc²(x))+e^xcot(x)]/[e^xcot(x)]²

Chain Rule

100

y = (3x²+2x-1)⁹

What is dy/dx = 9(3x²+2x-1)⁸(6x+2)

200

y = cos⁴(x)

What is dy/dx = -4cos³(x)sin(x)

300

y = sec(3e^x)

What is dy/dx = sec(3e^x)tan(3e^x)(3e^x)

400

y = sin(e^x2)

What is dy/dx = cos(e^x2) e^x2(2x)

500

y = sqrt(cos²(x))e^2x

What is dy/dx = 2sqrt(cos²(x))e^2x+e^2xcos(x)sin(x)/sqrt(cos²)

Implicit Differentiation

100

2x²+y³ = 3

What is dy/dx = -4x/3y²

200

x²y = 10x

What is dy/dx = (10-2xy)/x²

300

cos(xy) = y²

What is dy/dx = (2y + sin(xy))/(-ysin(xy))

400

cot(x/y)= y

What is dy/dx = (ycsc²(x/y))/[xcsc²(x/y)-y²]

500

(x²+y²)² = cos(e^y)

What is dy/dx = [-4x(x²+y²]/[4y(x²+y²)+sin(e^y)e^y]

Pop Culture

100

This MLB team was the first to introduce a live mascot in 1964.

Who are the New York Mets?

200

"You May be Right" If you guessed that this artist won his first Grammy Award in 1978.

Who is Billy Joel?

300

This is the highest grossing movie of all time when adjusted for inflation. 

What is "Gone with the Wind"?

400

The largest state in the USA by land mass

What is Alaska?

500

Number of future presidents that signed the declaration of independence

What is 2?